Introduction to Inequalities

Show your work for each problem.

1.
Which symbol means 'greater than'?
1. a)
2. b)
3. c)
4. d)
Answer:
The symbol means 'greater than'. The open side of the symbol faces the larger value.
2.
Is the statement true or false?
1. a)True
2. b)Cannot be determined
3. c)False
4. d)Neither
Answer: True
True. The statement reads '5 is less than 9', which is correct because 5 is smaller than 9.
3.
Fill in or :
Answer: >
because 12 is greater than 7. The symbol opens toward the larger number.
4.
Fill in or :
Answer: <
because 3 is less than 8. The pointed end of the symbol points to the smaller number.
5.
What does the symbol mean?
1. a)Not equal to
2. b)Less than
3. c)Greater than or equal to
4. d)Less than or equal to
Answer: Less than or equal to
means 'less than or equal to'. The line underneath the adds the possibility of equality.
6.
Which statement is TRUE?
1. a)
2. b)
3. c)
4. d)
Answer:
is true. On the number line, is to the LEFT of , so is smaller. Think: is colder than .
7.
Fill in or :
Answer: <
because is further left on the number line. Think of temperature: is colder (smaller) than .
8.
Is the statement true or false?
1. a)False
2. b)Only true if less than
3. c)True
4. d)Only true if equal
Answer: True
True! is true because 7 equals 7. The symbol means 'less than OR equal to', and the 'equal to' part is satisfied.
9.
A ride requires you to be at least 130 cm tall. Write this using for height (use >= or <=).
Answer: h >= 130
means height must be 130 cm or more. 'At least' translates to because 130 is allowed.
10.
Order from least to greatest: , , ,
Answer: -7, -4, 1, 3
1. Which number is furthest left on the number line (smallest)? -7
2. Which is the next smallest number? -4
3. Which positive number comes next? 1
4. Which is the largest (furthest right)? 3
11.
You have 30 euros and want to buy a book for 12 euros and a toy. What's the maximum price for the toy? Write and solve the inequality.
Answer: 18
1. What is your total budget? 30
2. How much does the book cost? 12
3. If the toy costs euros, write the inequality: ? 30
4. Solve for : What is the maximum value? 18
12.
Which value does NOT satisfy ?
1. a)
2. b)
3. c)
4. d)
Answer:
does NOT satisfy because . The other values (0, -2, 10) are all greater than or equal to -2.
13.
Write an inequality: A pool requires children to be less than 10 years old for free entry. Use for age.
Answer: a < 10
because 'less than 10' means ages 9 and below. A 10-year-old would NOT get free entry, so we use not .
14.
A speed limit sign shows 'Maximum 80 km/h'. A car is traveling at 85 km/h. Is the driver breaking the law? Explain using inequalities.
Answer: yes
1. What does 'maximum 80 km/h' mean? Write the rule as an inequality using for speed. v <= 80
2. What speed is the car traveling? 85
3. Is true or false? false
4. Is the driver breaking the law? (yes/no) yes
15.
Put these numbers in order from greatest to least: , , , ,
Answer: 5, 2, 0, -1, -6
1. Which number is the greatest (furthest right on number line)? 5
2. Which is the next greatest? 2
3. What number comes between positive and negative? 0
4. Which negative number is closer to zero? -1
5. Which is the smallest (furthest left)? -6
16.
Which inequality correctly represents: 'You must be at least 13 but under 18 to join the youth club'?
1. a)
2. b)
3. c)
4. d)
Answer:
is correct. 'At least 13' means age 13 is allowed (), and 'under 18' means 18 is NOT allowed ().